(141b) Reduced Order CFD Model By an Asymptotic Expansion for Heterogenous Catalysis

Computational Fluid Dynamics (CFD) analysis of reactive flows over heterogeneous catalysts is a challenging task even for “simple” laminar flows. This involves solving a system of Partial Differential Equations (PDEs) with highly non-linear boundary conditions imposed by the surface chemistry which leads to stiffness and bad conditioning of the overall equation system requiring extensive computational effort. Moreover, the recent development of experimental techniques which provide spatially resolved atomistic scale information of the catalyst under operando conditions makes it possible to derive the underlying catalytic kinetics by solving an inverse problem (which would be only plausible) with a computationally less intensive CFD analysis for such catalytic reactors.

In this study, we present a reduced order approach with a significant lower computational footprint than conventional CFD, which caters for systems with heterogeneous catalytic reactions occurring only at the walls of the reaction chambers where the area of the catalyst is small as compared to the entire flow domain. The approach would be applicable to general reactor geometries and in the scope of 3D printing. Examples of such systems would be the catalyst characterization chambers or catalytic monoliths.

The approach is based on the observation that in many experiments the mixture density and the species transport coefficients are hardly affected by the surface chemistry. The velocity field then decouples from the chemistry and can be obtained from the non-reactive flow problem. This assumption becomes exact in the limit of low chemical reactivity and for excess of one or more species. Focusing on the assumption before, we exploit the fact that in the case of small catalyst limit, the lateral variation of the reactivity on the catalytic surface will be small. So, a leading order asymptotic series expansion for these species results in a problem, which can be solved by three simple steps. First, calculating the velocity field from the non-reactive solution. Second, obtaining the solution of a linear transport problem with constant reactivity. Finally, parametrically feeding of the solution into a small non-linear algebraic problem, which has as many unknowns as species.

The approach has been implemented using VoronoiFVM [1] Finite Volume package programmed in Julia, which guarantees mass conservation. We will demonstrate the approach using the Methanol formation reaction from CO₂ and H₂ and for flow geometries where the zero-reactivity solution for the velocity field is known. Using these, the strengths and limitations of the approach are addressed. The proposed approach is benchmarked against numerical simulations of the fully coupled problem using the CatalyticFoam solver [2,3].

Acknowledgements

We thank the Elsa Neumann Stipendium (Nachwuchsförderungsgesetz NaFöG) and Higher Education Comission Pakistan (ID 57589483) for their financial support for this project.

References:

¹Fuhrmann, J.; Abdel, D.; Weidner, J.; Seiler, A.; Farrell, P.; Liero, M. VoronoiFVM.jl - Finite volume solver for coupled nonlinear partial differential equations; https://github.com/j-fu/VoronoiFVM.jl; doi:10.5281/zenodo.3529808

²Maestri, M.; Cuoci, A, J. Coupling CFD with detailed microkinetic modeling in heterogeneous catalysis; Chemical Engineering Science; 2013; pp 106-117; doi.org/10.1016/j.ces.2013.03.048

³OpenFOAM,2011. 〈www.openfoam.org〉.